Lyapunov-based stability analysis for REM congestion control

This paper investigates convergence properties of basic REM flow control algorithm via Lyapunov functions. The decentralized algorithm REM consists of a link algorithm that updates a congestion measure, also called "price", based on the excess capacity and backlog at that link, and a source algorithm that adapts the source rate to congestion in its path. At the equilibrium of the algorithm, links are fully utilized, and all buffers are cleared. Convergence of the algorithm is established for single and two-link cases using a Lyapunov argument. Extension to the general multi-link model is discussed as well.